These are two parts with 5 questions each.
Part 1.] Match the y-coordinate with the given x-coordinate for the equation [tex]y=log_{10}x[/tex]
If you use this property you can match all the coordinates:
[tex]log_{a}a^{x}=x[/tex]
Because that means that: [tex]log_{10}(10)^{x}=x[/tex]
So, just write each x-coordinate as a power of 10.
1.) 1/100 = 10^(-2)
2.) 1/10 = 10 ^ (-1)
3.) 1 = 10 ^ (0)
4.) 10 = 10^(1)
5.) 100 = 10^(2)
With that you find:
x-coordinate y-coordinate
[tex]y=log_{10}x[/tex]
1/100 [tex]log_{10}(1/100) = - 2 [/tex] => 1) matches B)
1/10 [tex]log_{10}(1/10)=-1[/tex] => 2) matches D)
1 [tex]log_{10}1=0[/tex] => 3) matches A)
10 [tex]log_{10}10=1[/tex] => 4) matches E)
100 [tex]log_{10}100=2[/tex] => 5) matches C)
Part 2.] Match the y-coordinate with the given x-coordinate for the equation [tex]y=log_{2}x[/tex]
Using the same property of logarithms: [tex]log_{2}2^{x}=x[/tex]
And:
1.) 8 = 2^(3)
2.) 4 = 2^(2)
3.) 2 = 2^(1)
4.) 1 = 2^(0)
5.) 1/2 = 2^(-1)
So:
x y = [tex]y=log_{2}x[/tex]
8 [tex]y=log_{2}8=3[/tex] => matches C)
4 [tex]log_{2}4=2[/tex]=> matches A)
2 [tex]log_{2}2=1[/tex] => matches B)
1 [tex]log_{2}1=0[/tex] => matches D)
1/2 [tex]log_{2}(1/2)=-1[/tex] => matches E)
